MAT 362  Differential Geometry of Surfaces   Spring 2010  TuTh 12:50pm - 2:10pm Physics P117

Instructor: Ljudmila Kamenova
Office: Math Tower 3-115
Office hours: Wed 9:30 - 11:30 a.m. in Math 3-115, Wed 1:30 - 2:30 in the MLC

The Instructor may be reached by e-mail at kamenova@math.sunysb.edu.
Feel free to send me an e-mail or drop by outside of office hours.

Course Description: The foundation of differential geometry is the concept of curvature. The course will focus on understanding this and related concepts very clearly, both geometrically and computationally, for the case of surfaces in Euclidean space. For this, you'll need a solid background in multivariable calculus and linear algebra. We hope to give some idea of how curvature is understood in higher dimensions; this is the basis of Riemannian geometry and General Relativity.

Prerequisites: MAT 205 (Calculus III) and MAT 210 (Linear Algebra).

Text: M. do Carmo, Differential Geometry of Curves and Surfaces, Prentice Hall (1976)

Other books:
• A. Pressley, Elementary Differential Geometry, Springer, 2001.
• B. O'Neill, Elementary Differential Geometry.
• Millman and Parker, Elements of Differential Geometry.

Grading: There will be one midterm exam (on 03/18 in class) and a final exam (on 05/13, 5:15 - 7:45 p.m.). There will be regular homework assignments, due roughly once per week. Your grade will be determined via the following percentages: homework: 50%, midterm: 20% and final: 30%.

Homework:

HW 1 (due on Feb. 4th): [Do Carmo] Section 2.2, Problems 1, 4, 7(a)(b), 10, 11(a) and 16

HW 2 (due on Feb. 11th): [Do Carmo] Section 2.3, Problems 2, 3, 4 and 5

HW 3 (due on Feb. 18th): [Do Carmo] Section 2.4, Problems 1, 2, 3 and 7

HW 4 (due on Feb. 25th): [Do Carmo] Section 2.5, Problems 3, 4, 5, 9 and 10

HW 5 (due on March 4th): [Do Carmo] Section 2.6, Problems 1, 2 and 4

HW 6 (due on March 11th): [Do Carmo] Section 3.2, Problems 2, 3, 8 and 17

HW 7 (due on March 25th): [Do Carmo] Section 3.3, Problems 1 and 13

HW 8 (due on April 15th): [Do Carmo] Section 4.2, Problems 1 and 2; Section 4.3, Problems 3 and 4

HW 9 (due on April 29th): [Do Carmo] Section 4.4, Problems 4 and 15

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